The reformulated problem aims at shaping the distribution \(p_\theta \)  so as to put all its mass on a minimizer \(P^*\)  of \(\widetilde{\mathcal {W}}_2^2\) , thus integrating the use of Bayesian exploration in the optimization process. This approach is commonly used in many areas of stochastic search, such as evolution strategies [1]}, [2]}, [3]}.
